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Time-Fractional Heat Conduction with Heat Absorption in a Half-Line Domain Due to Boundary Value of the Heat Flux Varying Harmonically in Time

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

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Abstract

The time-fractional heat conduction equation with heat absorption is considered in a half-line domain under the mathematical and physical Neumann boundary conditions varying harmonically in time. The Caputo derivative is employed. The Laplace transform with respect to time and the cos-Fourier transform with respect to the spatial coordinate are used. The solutions are obtained in terms of integrals with integrands being the Mittag-Leffler functions. The numerical results are illustrated graphically.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200, Czestochowa, Poland

    Yuriy Povstenko

  2. Institute of Law, Administration and Management, Jan Dlugosz University in Czestochowa, Zbierskiego 2/4, 42-200, Czestochowa, Poland

    Tamara Kyrylych

Authors
  1. Yuriy Povstenko
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  2. Tamara Kyrylych
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Correspondence to Yuriy Povstenko .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Povstenko, Y., Kyrylych, T. (2020). Time-Fractional Heat Conduction with Heat Absorption in a Half-Line Domain Due to Boundary Value of the Heat Flux Varying Harmonically in Time. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_20

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